A204244 Symmetric matrix given by f(i,1)=1, f(1,j)=1, f(i,i)=i! and f(i,j)=0 otherwise.

1, 1, 1, 1, 2, 1, 1, 0, 0, 1, 1, 0, 6, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 24, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 120, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 720, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 5040, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0

Offset: 1

Author

Clark Kimberling, Jan 13 2012

Keywords

• nonn
• tabl

Examples

			Northwest corner:
1 1 1 1
1 2 0 0
1 0 6 0
1 0 0 24
		

Crossrefs

Cf. A204245, A203228.

Programs

Mathematica

f[i_, j_] := 0; f[1, j_] := 1; f[i_, 1] := 1; f[i_, i_] := i!;
m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
TableForm[m[8]] (* 8x8 principal submatrix *)
Flatten[Table[f[i, n + 1 - i],
  {n, 1, 12}, {i, 1, n}]]      (* A204244 *)
Table[Det[m[n]], {n, 1, 15}]   (* A204245 *)
Permanent[m_] :=
  With[{a = Array[x, Length[m]]},
   Coefficient[Times @@ (m.a), Times @@ a]];
Table[Permanent[m[n]], {n, 1, 14}]   (*  A203228 *)